SOLUTION: Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference:
a. ∗ +56a+49
b. 25a^2+ ∗ + 1/4^2
c. 0.01b^2+ ∗ +1
Algebra.Com
Question 1122671: Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference:
a. ∗ +56a+49
b. 25a^2+ ∗ + 1/4^2
c. 0.01b^2+ ∗ +100c^2
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
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25a^2+ ∗ + 1/4^2
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You want to start with a squared binomial and the leading and ending terms of the trinomial product make this binomial obvious.
Do what more you know you need.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Has to be the square of a SUM because all the signs are positive. The second term of the sum must be the square root of the last term, namely 7. The missing term must have an 
in it. And the coefficient on the middle term is the coefficient on the first term of the binomial times the last term of the binomial times 2. So 56 divided by 2 is 28, and 28 divided by 7 is 4.
^2\ =\ \underline{16a^2}\ +\ 56a\ +\ 49)
John
My calculator said it, I believe it, that settles it
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